Primary decomposition of ideals (submodule) in BCK-algebras
نویسندگان
چکیده
In this paper, we investigate the ideal theory in BCK-algebras and we define the notions of primary and P -primary ideals. Then we show that in bounded implicative BCK-algebras, if an ideal has a primary decomposition, then it has a reduced primary decomposition. In the follow, we extend the above concepts to X-modules (Extended BCK-modules) and we introduce the notions of primary and P -primary submodules. Finally, we prove that if X is a lower BCK-semilattice and M is a Noetherian X-module, then every proper submodule of M has a reduced primary decomposition.
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